How can I fix my rotation issues of an object following a path?
Simplified Bird and Circle Path. 


Know that your final location and orientation is a combination of the displayed bird rotation and the effects of the Path Constraint [PC]
Choose correct origin for the bird. This might be middle of body. Perhaps near spine.
Remove all location and rotation keyframes for the bird for initial phase.  This eliminates competing animations. Fresh start.
For the initial phase your bird can start at the origin
Enable the Follow Curve option of Path Constraint [PC]
If need be choose correct initial rotation of the bird.  Typically in degrees one of 0, 90, 180, 270 in object mode on one or more axis.  You may want to keyframe this as a safe starting position at a known reserved frame number X. 
Enable Fixed position in the [PC].  Set keyframes in [PC] for offset.
If the bird is always consistently tangent (lined up) to the curve you are golden.  If not allow your self one additional rotation keyframed on the aforementioned reserved frame number X.
Get the above steps to work. Archive File and consider more complex animations later.